Method of determining the density profile

ABSTRACT

A method of determining the density profile of a plate-shaped material M, the density of which varies discretely or continuously across the plate thickness, whereas the density at a specific depth of the plate M is preferably assumed to be constant. The inventive method employs X-rays or γ-rays from a source K. The latter source K is placed on one side of the plate M, whereas at least two detectors T, F are arranged on the opposite side of the endless plate being advanced during the measuring in the longitudinal direction. A first detector T is preferably placed in the radiating direction of the source and measures the transmittent radiation through the plate M, and the second detector F is placed outside the radiating direction of the source K and measures the scattered radiation on partial volumes along the radiating direction of the source. Based on the signals measured by the detectors it is possible to measure the density in each individual partial volume. According to the invention a compensation has furthermore been carried out for multiple scattered radiation by the measured radiation being deducted from the multiple scattered radiation.

TECHNICAL FIELD

The invention relates to a method of determining the density profile ofa plate-shaped material.

BACKGROUND ART

Danish Patent Application No. 0723/94 discloses a method of determiningthe density profile of plate-shaped materials by way of a measuring ofCompton-scattered radiation from small partial volumes in the material.During the measuring, a predetermined angular relation is maintainedbetween the incident and the scattered radiation, and the scatteredradiation is adjusted by a simultaneous measuring of the incidentradiation intensity and the attenuation in the entire plate-shapedmaterial. However, such a measuring method only makes allowance forsingly scattered radiation.

It is known from the article "The characterisation of multiplescattering in Compton profile measurements" by T. Pitkanen in NuclearInstruments and Methods i Physics Research A257 (1987) pp 384-390 thatmultiple scattered radiation is rather important in connection withrelatively thick plates.

BRIEF DESCRIPTION OF THE INVENTION

The object of the invention is therefore to provide a method ofdetermining the density profile of a plate-shaped material, said methodbeing more accurate than hitherto known.

A method of the above type is according to the invention characterizedby compensating for multiple scattered radiation in each partial volume.The resulting measuring method is far more accurate than hitherto known,especially in connection with relatively thick plates.

According to a particularly advantageous embodiment, the multiplescattered radiation is compensated for by said radiation being reducedby the measured radiation, as the multiple scattered radiation can befound on the basis of some parameter values provided by way of acalibration measur- ing.

BRIEF DESCRIPTION OF THE DRAWING

The invention is explained in greater detail below with reference to theaccompanying drawing, in which

FIG. 1 illustrates how the measured intensity of the scattered radiationis composed of several values,

FIG. 2 shows a measuring arrangement wherein an additional detector iscoupled between the X-ray source and the plate-shaped material,

FIG. 3 shows an arrangement of two plate-shaped materials arranged at amutual distance, and

FIG. 4 shows an example of how one of the parameter values β variesversus the height of the plate material.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 shows how the measured intensity of the scattered radiation iscomposed of contributions from the considered partial volume at P andcontributions from multiple scattered radiation either in theplate-shaped material M itself, where scattered radiation from theentire length AB can cause a renewed scattering from the length CD in adirection towards the detector F, or via a collimator where scatteredradiation from the length AB meets the wall of said collimator and isscattered towards the detector F.

The intensity of the multiple scattered radiation is not correlated withthe density of the partial volume at P, but almost unambiguouslycorrelated with the surface weight ρ of the plate-shaped material M,where ρ is the average density and t is the thickness.

The latter has been confirmed by simulation calculations performed bythe known Monte-Carlo-method. For the present measuring geometry with anarrow incident beam and a strong collimation in front of the detectorfor scattered radiation and an optical thickness of μ·ρp·t≦1, where μ isthe absorption coefficient, the intensity of multiple scatteredradiation I_(MS) can be approximately expressed by

    I.sub.MS =βI.sub.0 μ·ρ·t(1-α·μρt)(1)

where I₀ is the incident intensity.

I_(MS) is proportional to the intensity I₀ of incident radiation, andthe parameters α and β depend on the actual measuring geometry (theextent of the beam, the visual field of and the distance to thecollimator and the detector etc. Furthermore, β depends on the positionof P of the actual partial volume, from which singly scattered radiationis to be measured. When the location P₁ is considered outside the plateM, a definite probability applies of multiple scattered radiation overthe length AB through C', D' or E' to the staggered detector. I_(MS)decreases, however, proportional to an increasing distance to C', D'from AB.

The above observations result in a possibility of compensating formultiple scattered radiation in the following manner.

As shown in FIG. 2, a detector TK is placed between the X-ray source Kand the plate-shaped material M. The detector TK measures thetime-related variation of the intensity of the source K. Together, themeasuring signal from the detector TK and the transmitted measuringsignal T provide the relation ##EQU1## where μ is the absorptioncoefficient, ρ is the density, and t is the thickness, whereafter theadjusted density ρ_(korr) is found for a partial volume at P accordingto Danish patent application No. 0723/94 by a deduction of I_(MS) (P) as##EQU2## where T=I₀ e⁻μρt or TK=I₀ ·k (k=constant fraction of theintensity of the X-ray tube measured as I₀ at T for an empty measuringgap) has been adjusted by the factor k.

The parameters α, β are determined by way of a calibration measuring forthe actual measuring arrangement. In FIG. 3 two plates M', M" areinterspaced a distance corresponding to the length of approximatelythree partial volumes. When I_(FS) is measured from the resulting airgap between the plates M', M", only multiple scattered radiation ismeasured. The measuring of I_(FS) is repeated with another set of plates(larger/smaller thickness and/or higher/lower density), which results intwo equations with two unknown quantities for determining α and β. Thevariation of β with P relative to the central value is subsequentlydetermined by means of a set of plates of thicknesses corresponding to3-4 partial volumes, between which an air gap is established at variousdepths.

As the effect of multiple scattered radiation is vague (approximately10% corresponding to the value of α) of singly scattered radiationmeasured in a typical measuring object of a density of approximately 1g/cm³), it is sufficient to know the absolute contribution at the centreof the plate-shaped material. Subsequently the relative variation of βfrom the lower edge to the upper edge measured for one thickness can beutilized for calculating the multiple scattering contribution acrossplates of an arbitrary thickness.

In practice, the density profile measuring device is supplemented withan optical thickness meter, such as an optical reflection meter, wherebyboth the size ##EQU3## as the thickness t are found in a computer at thebeginning of the production and are continuously updated. Based on thethickness t the position of the detector F is calculated, said positioncorresponding to "0", "1/2 t" and "t". As far as the central positioncorresponding to 1/2 t is concerned, the values of α and β are takenfrom a table. A function β(P) renders it possible to calculate therelative variation of β across the measured thickness, whereafter themeasured scattering densities are adjusted by means of formula (2).

The selection of angle of incidence and scattering angle as well as theutilization of the signals from the three detectors follow the methodaccording to Danish patent application No. 0723/94.

A γ-ray source may be used instead of an X-ray source.

What is claimed is:
 1. A method of determining the density profile of aplate-shaped material (M), the density of which varies discretely orcontinuously across the plate thickness, whereas the density at aspecific depth of said plate is preferably assumed to be constant, bymeans of X-rays or γ-rays from a source (K) being arranged on one sideof said plate (M), whereby at least two detectors (T, F) are arranged onthe opposite side of the plate being advanced during measuring in thelongitudinal direction, one first detector (T) preferably being placedin the radiating direction of the source (K) so as to measure theradiation transmitted through the plate (M), and at least one detector(F) being placed outside the radiation direction of said source (K) soas to measure the radiation scattered from partial volumes along theradiating direction of the source (K), wherein multiple scatteredradiation in each individual partial volume is compensated for bysubtracting the multiple scattered radiation from the measuredradiation, said multiple scattered radiation being calculated by meansof the formula

    I.sub.MS =βI.sub.0 μ·ρ·t(1-α·μρt)

where I₀ represents incident intensity, and α and β depend on measuringarrangement, and wherein a relative variation of β is determined bymeans of a number of sets of plates of thicknesses corresponding to anumber of partial volumes, an air gap being established between saidplates at various depths.
 2. The method as claimed in claim 1, whereincalibration is achieved by means of at least two sets of plates with agap between the plates for determining α and β from two equationscontaining α and β.
 3. A method for determining a density profile of aplate (M), the density of which varies across a thickness of said plate,by means of radiation from a source arranged on one side of said plate,with at least two detectors being arranged on a side of said plateopposite from said source, a first detector being placed in a radiatingdirection of the radiation source so as to measure radiation transmittedthrough said plate (M), and a second detector being placed outside theradiation direction of said radiation source so as to measure radiationscattered from partial volumes along the radiating direction of saidsource, wherein multiple scattered radiation in each individual partialvolume is compensated for by subtracting the multiple scatteredradiation from the measured radiation, said multiple scattered radiationbeing calculated by means of a formula

    I.sub.MS =βI.sub.0 μ·ρ·t(1-α·μρt)

where I₀ represents incident intensity, and α and β depend on measuringarrangement, and wherein a relative variation of β is determined bymeans of a number of sets of plates of thicknesses corresponding to anumber of partial volumes, an air gap being established between saidplates at various depths.
 4. The method as set forth in claim 3, whereindensity at a specific depth of said plate (M) is assumed to be constant.5. The method as set forth in claim 4, wherein at least said plate (M)is wood-based.
 6. The method as claimed in claim 3, wherein calibrationis achieved by means of at least two sets of plates with a gap betweenthe sets of plates for determining α and β from two equations containingα and β.
 7. The method as claimed in claim 3, wherein the source ofradiation is an X-ray source.
 8. The method as claimed in claim 3,wherein the source of radiation is a γ-ray source.